On 08/30/10 03:09 AM, Tim Daly wrote:
Bill Hart wrote:
Why is this entire thread not on sage-flame? What does software
engineering, documentation, test code, etc. have to do with "Creating
a viable free open source alternative to Magma, Maple, Mathematica and
Matlab."?
Despite what appears to be competitive badgering I really do want Sage
to succeed.
But I don't want Sage to spread the impression that mathematical
software can't be trusted.
I don't think mathematical software can be trusted - at least not 100%. But then
no code can.
Humans make errors, and if I recall correctly there's a 10^-18 chance of an
uncorrected bit error in the CPU I use (Xeon 3.33 GHz W3580). When you think of
the clock rate, errors are probably more frequent that we would like.
In any case, I don't think the world at large will judge mathematical software
on the basis of Sage. People are not going to say "I don't trust Mathematica,
Maple or MATLAB" since errors have been found in Sage.
One thing to be aware of is the probability of errors in tables you use - but
them I'm sure you are aware of that. Wolfram Research claim to have found
numerous errors in tables in maths books. Of course, in general they don't do
the ethical thing and report such errors in a way that everyone can verify their
claims, and if correct put a line though that result in the their book.
But there are exceptions.
http://library.wolfram.com/infocenter/TechNotes/4196/
has a title of "Errors found by Mathematica in Gradshteyn and Ryzhik, "Tables of
Integrals, Series, and Products" (4th Edition)."
The contents are just a text file
http://library.wolfram.com/infocenter/TechNotes/4196/GradshteynRyzhik.txt
If Sage is going
to be the M$ of mathematical software, will it also convince everyone
that math software
just gives highly questionable answers? Every program makes mistakes but
hand-waving
about "it's not my problem, it's the upstream code" gives the whole
field a bad reputation.
No, doing that gives Sage a bad reputation - you can not generalise that to all
mathematical software. Robert's statement, which I suspect he wishes he had not
made, would enhance the reputation of other software packages in comparison to
Sage.
As strange as he is, and as irritating as he is some times, Vladimir Bondarenko
has shown that there are numerous bugs in Maple and Mathematica. I don't know
all the techniques he uses (he keeps them secret as he hopes to market his
software), though I could postulate at some of them.
Many of the things Tim and David say resonate with me. I'd really,
really love a tremendously efficient, well-documented, reliable, Open
Source mathematical project. Having seen how insanely difficult even
just goal number 1 is for just the domain of arithmetic, I honestly
think we haven't got a chance. Not ever. The expertise don't exist in
sufficient quantity. And even those with the expertise, don't have the
time. So, looks like we are stuck with what we got.
I think sage's mission statement is overly optimistic.
I don't believe for one minute that Sage can ever become a viable alternative
for many people. It no doubt is for some. But that does make Sage useless. If I
thought Sage was useless, I would not bother subscribing to sage-devel and not
devote a considerable time to porting Sage to Solaris.
"Testing programs" is as ineffective as "testing theorems".
No matter how many examples you create, you don't have a proof.
Tim Daly
Tim, you make some good points. You are clearly a talented person in your field.
But I suspect that it's simply not practical for the Sage community, Wolfram
Research, Mathworks to prove their code correct. All such projects we grind to a
snail's pace if they tried to do it. You need to be realistic about what is, and
what is not reasonably practical.
I know Sage does not have an aim to execute Mathematica programs directly, but
it would be incredibly useful if there was a Mathematica -> Sage translator. The
Rubi test suite is already available in Mathematica format. Creating such a tool
would be an interesting student project. Unfortunately, it would require
knowledge of Sage, Mathematica, parsers and a whole lot of other skills that
would probably be hard to find in one individual student.
Dave
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